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We analyze the relationship between the experimentally observed pressure gradients at resonant rational surfaces and the theoretically predicted ideal magnetohydrodynamics (MHD) unstable region of global modes in the large helical device (LHD). According to the stability analysis of the ideal MHD modes with a low toroidal mode number, we find that the ideal MHD mode gives a constraint on the operational regime of the pressure gradients in the core. In the edge, a clear saturation of the pressure gradients due to the ideal MHD instability has not been observed up to the high beta regime around 3% as the volume-averaged toridal beta value, where global ideal MHD modes are predictedto be unstable.

Ideal MHD yields at best inconclusive predictions about the stability of the LHD heliotron for $\langle \beta \rangle \geq 3\%$. We investigate the impact of the drift stabilization of ballooning modes for the inward shifted LHD configuration (vacuum magnetic axis $R_0 \sim 3.5m $). The background equilibrium is considered anisotropic in which the neutral beam ions contribute about $1/4$ fraction of the total diamagnetic beta, $\langle \beta_{dia} \rangle$. A drift corrected ballooning mode equation obtained from the linearized gyrokinetic equation is expanded assuming that the hot particle drifts are much larger than the mode frequency. The fast particle pressure gradients contribute weakly to both the instability drive and the diamagnetic drift stabilization (which is dominated by the thermal ion diamagnetic drifts) for $\langle \beta_{dia} \in [0,4.8] \%$. In the single fluid limit (diamagnetic drifts ignored), the thermal pressure gradients drive ballooning modes in a broad region encompassing the outer $60-90 \%$ of the plasma volume at $\langle \beta_{dia} \rangle \approx 4.8 \%$. To stabilize these modes, we find that diamagnetic drift corrections must be invoked (mainly due to the thermal ions). The energetic ion diamagnetic drifts play a role only for low wave number values, $k_{\alpha}\leq 8$. It has been verified that the fast particle drift ordering imposed by the model is amply satisfied for on-axis hot particle to thermal density $N_{h0}/N_{i0} \approx 1\%$ even at high $\langle \beta_{dia} \rangle$.